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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

Extreme and exposed points of spaces of integral polynomials


Authors: Christopher Boyd and Silvia Lassalle
Journal: Proc. Amer. Math. Soc. 138 (2010), 1415-1420
MSC (2010): Primary 46G25; Secondary 46B04
Published electronically: November 3, 2009
MathSciNet review: 2578533
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Abstract: We show that if $ E$ is a real Banach space such that $ E'$ has the approximation property and such that $ \ell_1\not\hookrightarrow {\widehat \bigotimes_{n,s,\epsilon}} E$, then the set of extreme points of the unit ball of $ \mathcal{P}_I(^nE)$ is equal to $ \{\pm\phi^n\colon \phi\in E',\Vert\phi\Vert=1\}$. Under the additional assumption that $ E'$ has a countable norming set, we see that the set of exposed points of the unit ball of $ \mathcal{P}_I(^nE)$ is also equal to $ \{\pm\phi^n\colon \phi\in E',\Vert\phi\Vert=1\}$.


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Additional Information

Christopher Boyd
Affiliation: School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland
Email: Christopher.Boyd@ucd.ie

Silvia Lassalle
Affiliation: Departamento de Matemática, Pab. I – Cuidad Universitaria (FCEN), Universidad de Buenos Aires, (1428) Buenos Aires, Argentina
Email: slassall@dm.uba.ar

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10158-2
Keywords: Integral polynomials, exposed points, extreme points
Received by editor(s): February 3, 2009
Received by editor(s) in revised form: August 11, 2009
Published electronically: November 3, 2009
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.